$\overleftrightarrow{A B}$ and $\overleftrightarrow{C D}$ are parallel lines

Which translation of the plane can we use to prove angles $x$ and $y$ are congruent, and why?

Choose 1 answer:
(A) A translation along the directed line segment $C B$ maps line $\overleftrightarrow{C D}$ onto line $\overleftrightarrow{A B}$ and angle $y$ onto angle $x$.
(B) A translation along the directed line segment $A C$ maps line $\overleftrightarrow{A B}$ onto line $\overleftrightarrow{C D}$ and angle $x$ onto angle $y$.
C) A translation along the directed line segment $A B$ maps line $\overleftrightarrow{C D}$ onto line $\overleftrightarrow{A B}$ and angle $y$ onto angle $x$

Question

$\overleftrightarrow{A B}$ and $\overleftrightarrow{C D}$ are parallel lines

Which translation of the plane can we use to prove angles $x$ and $y$ are congruent, and why?

Choose 1 answer:
(A) A translation along the directed line segment $C B$ maps line $\overleftrightarrow{C D}$ onto line $\overleftrightarrow{A B}$ and angle $y$ onto angle $x$.
(B) A translation along the directed line segment $A C$ maps line $\overleftrightarrow{A B}$ onto line $\overleftrightarrow{C D}$ and angle $x$ onto angle $y$.
C) A translation along the directed line segment $A B$ maps line $\overleftrightarrow{C D}$ onto line $\overleftrightarrow{A B}$ and angle $y$ onto angle $x$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Given that lines $ \overleftrightarrow{AB} $ and $ \overleftrightarrow{CD} $ are parallel, and EF is a transversal, angles $x$ and $y$ are corresponding angles. ‖ ‖ step 2 ⋮ Corresponding angles are congruent if the lines are parallel and they are cut by a transversal. ‖ ‖ step 3 ⋮ A translation is a transformation that slides every point of a figure the same distance in the same direction. ‖ ‖ step 4 ⋮ To prove angles $x$ and $y$ are congruent using translation, we need to slide line $ \overleftrightarrow{CD} $ onto line $ \overleftrightarrow{AB} $ such that angle $y$ coincides with angle $x$. ‖ ‖ step 5 ⋮ The translation along the directed line segment $CB$ will map line $ \overleftrightarrow{CD} $ onto line $ \overleftrightarrow{AB} $ and angle $y$ onto angle $x$. ‖ ***A*** ∻Key Concept∻ ⚹Translations and Corresponding Angles⚹ ∻Explanation∻ ⚹When parallel lines are cut by a transversal, corresponding angles are congruent. A translation that maps one line onto another and one angle onto another can be used to prove the congruence of those angles.⚹◊How do translations along directed line segments affect parallel lines and angles formed by a transversal⍭ Generate me a similar question◊

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